Bertini irreducibility theorems over finite fields
نویسندگان
چکیده
منابع مشابه
Bertini Irreducibility Theorems over Finite Fields
Given a geometrically irreducible subscheme X ⊆ PnFq of dimension at least 2, we prove that the fraction of degree d hypersurfaces H such that H ∩X is geometrically irreducible tends to 1 as d→∞. We also prove variants in which X is over an extension of Fq, and in which the immersion X → PnFq is replaced by a more general morphism.
متن کاملBertini Theorems over Finite Fields
Let X be a smooth quasiprojective subscheme of P of dimension m ≥ 0 over Fq. Then there exist homogeneous polynomials f over Fq for which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to ζX(m + 1) −1, where ζX(s) = ZX(q −s) is the zeta function of X. An analogue for regular quasiprojective schemes over Z is proved, assuming ...
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Constructing r -th nonresidue over a nite eld is a fundamental computational problem. A related problem is to construct an irreducible polynomial of degree r e (where r is a prime) over a given nite eld Fq of characteristic p (equivalently, constructing the bigger eld Fqr e ). Both these problems have famous randomized algorithms but the derandomization is an open question. We give some ne...
متن کاملIrreducibility and r-th root finding over finite fields
Constructing r-th nonresidue over a finite field is a fundamental computational problem. A related problem is to construct an irreducible polynomial of degree re (where r is a prime) over a given finite field Fq of characteristic p (equivalently, constructing the bigger field Fqr ). Both these problems have famous randomized algorithms but the derandomization is an open question. We give some n...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2014
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2014-00820-1